You cannot revoke your fingerprint, but your fingerprint is just unlocking a private key. You can revoke that private key. So if you lose the YubiKey you can still revoke that YubiKey.
Correct, you can revoke the YubiKey itself, although the actual mechanism to do that is implemented by the web app you're authenticating with, not some central registry, so other than conventional expectations, your mileage may vary. You can also hopefully re-enroll the YubiKey after you change the fingerprint.
The new private key would still be unlockable with the same fingerprint.
Doesn’t matter, it’s in your possession. If you lose it, you revoke the yubikey.